Probing biomechanical properties with a centrifugal force quartz crystal microbalance

Aaron Webster,1, ∗ Frank Vollmer,1 and Yuki Sato21Max Planck Institute for the Science of Light, Günther-Scharowsky-Str. 1/Bau 24, Erlangen D-91058, Germany

2The Rowland Institute at Harvard, Harvard University,100 Edwin H. Land Boulevard, Cambridge, Massachusetts 02142, USA

(Dated: Wednesday 24th September, 2014)

Application of force on biomolecules has been instrumental in understanding biofunctional be-havior from single molecules to complex collections of cells. Current approaches, for example thosebased on atomic force microscopy or magnetic or optical tweezers, are powerful but limited in theirapplicability as integrated biosensors. Here we describe a new force-based biosensing techniquebased on the quartz crystal microbalance. By applying centrifugal forces to a sample, we show itis possible to repeatedly and non-destructively interrogate its mechanical properties in situ and inreal time. We employ this platform for the studies of micron-sized particles, viscoelastic monolayersof DNA, and particles tethered to the quartz crystal microbalance surface by DNA. Our results in-dicate that, for certain types of samples on quartz crystal balances, application of centrifugal forceboth enhances sensitivity and reveals additional mechanical and viscoelastic properties.

INTRODUCTION

There are few experimental techniques that allow thestudy of force on biological molecules. Among them, op-tical or magnetic tweezers and atomic force microscopes(AFMs) have provided much insight into the mechanicsof DNA, RNA and chromatin [1] [2] [3] [4], friction andwear in proteins [5] [6] and stepwise motion of motorproteins [7], all of which are important for understand-ing disease. However powerful, these methods have dif-ficulty operating as integrated devices to probe the me-chanical properties of heterogeneous samples in a widerange of applications in situ and in real time; tweezerand AFM experiments rely on highly trained experimen-talists, are not widely applicable as analytical tools, andare often constrained to the analysis of well prepared,homogeneous samples.

Among direct mechanical transduction methodsamenable for biosensing, the quartz crystal microbal-ance (QCM) has seen great utility as a simple, cost ef-fective, and highly versatile mechanical biosensing plat-form. Since its introduction by Sauerbrey [8] in 1959as a thin-film mass sensor in the gas phase, the under-standing and real-world applicability of these devices hasbeen repeatedly enhanced to study phenomena such asviscoelastic films in the liquid phase [9], contact me-chanics [10], and complex samples of biopolymers andbiomacromolecules [11].

Naturally, these benefits do not come without disad-vantages. The underlying mechanical properties of thesample that occur upon loading of the biomaterial areoften not revealed by the stepwise changes in the QCMsensorgram, an issue complicated by the choice of theo-retical model.

Here we introduce a novel QCM-based biosensing tech-nique which enables monitoring the mechanical response

∗ aaron.webster@mpl.mpg.de

of a sample to the continuous application of a variablecentrifugal force. This centrifugal force quartz crystalmicrobalance (CF-QCM) concept enables direct intro-duction of pico- to nanoscale forces in the liquid phasefor analyzing a sample’s mechanical properties. We showthat the response of a sample under centrifugal load isrevealing of its viscoelastic, mechanical, and conformalproperties.

RESULTS

Experiment

The experimental setup under consideration is shownschematically in FIG. 1(a). It consists of a QCM in-tegrated into the arm of a commercial swinging bucketcentrifuge. The QCM is connected in proximity to a re-mote driver which is tethered via a slip-ring connector toexternal data acquisition electronics. The crystal itselfis mounted in a holder radially by its edges such thatthe centrifugal force Fc is always normal to the surfaceof the crystal. On the sensing side of the crystal is a125 µL volume PDMS/glass cell containing the sample.The non-sensing side of the crystal remains in air. Whenin operation, the crystal and cell are mounted in eitherthe loading configuration, where the centrifugal force isin to the sensing side or, by mounting it upside down,in the unloading configuration, where the force is awayfrom the sensing side.An example CF-QCM response for free particles is de-

picted to the left in FIG. 1(b). Here, free 1 µm strep-tavidin coated polystyrene particles in water are intro-duced into the sample cell. When the cell is rotated tothe loading configuration under the influence of gravityalone, the particles fall toward the sensing surface and apositive shift in the QCM’s frequency signal is observed.When the cell is then rotated 180 degrees to the unload-ing configuration, the particles fall off and the frequencyresponse returns to its original state. Again the cell is

2

FIG. 1. Overview of the CF-QCM. (a) Experimental setup. A QCM and its driver are integrated into one arm of a stan-dard swinging bucket centrifuge. Data acquisition is done electrically through a tether and a centrally mounted slip ring.When spinning, centrifugal force is applied to a sample under assay. Here Fc ≡ m

√a2

c + a2g , where ac = ω2R and ag

are centripetal and gravitational accelerations, respectively. (b) Example CF-QCM experiment with 1 µm particles in water,NL = 1.58 × 1011 particle m−2, in the “loading” configuration (inset). The horizontal arrows indicate the motion of the QCM’stransverse shear mode. The spin up to 90 g in loading configuration enhances the QCM frequency shift signal and allowsextraction of mechanical properties of the sample, as well as particle size. See text for details.

rotated 180 degrees to the loading configuration and thepositive frequency shift is observed. As the centrifugespins up towards 90 g, the particles are “pressed” towardsthe QCM surface and a four fold increase in the frequencyshift is observed. The centrifuge then spins down and thebaseline frequency shift under gravity alone is recovered.

Traditional QCM experiments assume that the iner-tial properties and rigidity of the sample’s coupling aretaken as a fixed parameter (or statistical distribution)under assay. With this approach however, one is onlyable to obtain discrete values in an otherwise continu-ous parameter space. Hybrid-QCM experiments involv-ing nanoindenters [12] or AFM probe tips [13] have shownintriguing behavior when force is applied to a sample ina QCM measurement. There have also been reports thataccelerations as small as 1 g have a measurable effecton a QCM’s response for viscoelastic monolayers suchas DNA [14], and even for pure Newtonian liquids [15].All of these responses have been found to be significantcompared to the baseline acceleration sensitivity of theQCM itself [16]. With the integration of a centrifuge toa standard QCM, one can observe these effects under en-hanced g-forces and make endpoint measurements (mea-surements taken after the addition of a sample) in thesample’s parameter space continuously and repeatedly.

To demonstrate this, we have examined six differentsamples in the CF-QCM under variable accelerationsfrom approximately 1 g to 90 g. These samples were cho-sen to be examples of the breadth of load situations acces-sible with our technique. They are: (a) air, (b) deionizedwater, (c) free particles in water, (d) paramagnetic par-ticles attached to the sensor via short oligonucleotides,(e) 48 kbp lambda phage DNAs attached to the gold elec-trode, and (f) polystyrene particles tethered to the sensorvia 48 kbp lambda phage DNAs.

The employed QCM driver circuit outputs Butter-

worth van Dyke (BvD) equivalent relative frequency ∆f(in hertz) and motional resistance R (in ohms). R isapproximately related to the bandwidth Γ (half widthat half maximum of the frequency response) by Γ =R/ (4πL), where L = 40 mH is the motional inductance ofthe BvD equivalent circuit [17]. For this relationship weassume the small load approximation ∆f/fF 1, wherefF is the fundamental frequency [18]. It is therefore rele-vant to note our assumption that ∆R is an approximate,and indirect, measure of the bandwidth ∆Γ (in hertz). Inaddition ∆Γ is an equivalent representation of the “dis-sipation”, D, used in QCM-D devices by D = 2∆Γ/fF(See Supplementary Note 1).

The instrument’s response was first tested in air, shownin FIG. 2(a). The base acceleration sensitivity (change infrequency versus change in g-force) of AT cut quartz nor-mal to the plane of the crystal has a reported value [19] of∆f/∆g = 2.188(6)× 10−2 Hz g−1. Our instrument showssimilar behavior: ∆f/∆g = 2.682(23)× 10−2 Hz g−1 inthe loading configuration. The signs of ∆f/∆g are foundto be opposite in the loading and unloading configu-rations. We have not found a reference for the band-width or motional resistance dependence of a QCM un-der acceleration, but we find the value to be ∆Γ/∆g =9.203(171)× 10−4 Hz g−1.

Next, deionized water was used as a control sample formeasurement in the liquid phase, as shown in FIG. 2(b).The initial shift in frequency and bandwidth is in agree-ment with what is obtained the Kanazawa-Gordon rela-tions [9] for water (ρ = 1 g cm−3 and η = 1 mPa s): ∆f =−714 Hz and R = 359 Ω, which are close to the measuredvalues of ∆f = −716 Hz and R = 357 Ω. The responseunder centrifugal load was found to be linear and smallerthan that of air: ∆f/∆g = 1.357(24)× 10−2 Hz g−1 and∆Γ/∆g = 2.865(73)× 10−3 Hz g−1. We observe thatthese acceleration dependent forces in the liquid phase

3

0 20 40 60 80 100

−8

−6

−4

−2

0

2

4 (a)

g-force [g]

∆f

Air

−8

−6

−4

−2

0

2

4∆Γ

0 10 20 30 40 50 60 70 80 90

−8

−6

−4

−2

0

2

4 (b)

g-force [g]

∆f

Water

−8

−6

−4

−2

0

2

4∆Γ

0 20 40 60 80 100−30

−20

−10

0

10

20

30

40 (c)

g-force [g]

∆f

Free Particles

−30

−20

−10

0

10

20

30

40∆Γ

0 20 40 60 80 100−35

−30

−25

−20

−15

−10

−5

0

5 (d)

g-force [g]

∆f

Attached Particles

−35

−30

−25

−20

−15

−10

−5

0

5∆Γ

0 10 20 30 40 50 60 70

−20

−15

−10

−5

0

5(e)

g-force [g]

∆f

Lambda DNA

−20

−15

−10

−5

0

5∆Γ

0 10 20 30 40 50 60 70

−60

−50

−40

−30

−20

−10

0

10

20 (f)

g-force [g]

∆f

Tethered Particles

−60

−50

−40

−30

−20

−10

0

10

20∆Γ

∆f loading ∆f unloading ∆Γ loading ∆Γ unloading

FIG. 2. Load situations. Change in frequency ∆f and bandwidth ∆Γ (in hertz, inferred from motional resistance) of theCF-QCM under different load situations as the centripetal acceleration is directed in to (loading, represented by circles withthe top half colored) and out of (unloading, represented by circles with the bottom half colored) the plane of the crystal. Thesituations are (a) unloaded crystal in air, (b) deionized water, (c) free 1 µm diameter streptavidin coated polystyrene particles,NL = 1.58 × 1011 particle m−2, (d) 2 µm diameter streptavidin coated paramagnetic particles, NL = 1.65 × 1010 particle m−2,attached with 25 mer oligonucleotides, (e) lambda DNA only attached to the gold electrode, and (f) 25 µm diameter streptavidincoated polystyrene particles, NL = 3.25 × 107 particle m−2, tethered to the sensor surface with 48 kbp lambda DNAs. Errorbars are derived from uncertainties (standard deviation) in the centrifuge both spinning up and spinning down in a singleexperimental run.

are not necessarily commensurate with those in the gasphase, but as the effects are small compared to experi-ments with actual loads, we treat them as baselines tobe subtracted.

Utilizing the flexibility that the instrument providesin modifying the coupling between the load and thesensor surface, we have applied the technique to thestudy of discrete micron sized particles. As first refer-enced in FIG. 1(b), the frequency and bandwidth shiftsof free particles in the liquid phase as a function of g-force is shown in FIG. 2(c). Here, streptavidin coatedpolystyrene particles, mean diameter d = 1.07 µm, areplaced in the sample volume with a surface density ofNL = 1.58× 1011 particle m−2 and the signal is observedin both the loading and unloading configurations. Theparticles did not exhibit adhesion to either the unmod-ified gold electrode or the glass/PDMS cell surrounding

it; in the unloading configuration, the particles quicklydrifted away from the sensing area and a signal identicalto water was observed. In the loading configuration, alarge positive shift in ∆f and ∆Γ was observed, consis-tent with previously observed responses for weakly cou-pled particles in this size range [10].The initial shift under 1 g was found to be ∆f = 2.2 Hz

and ∆Γ = 7.5 Hz. At the maximum acceleration of 90 gthe signal increases to ∆f = 16.5 Hz and ∆Γ = 37 Hz.This also represents a sensitivity enhancement in theminimum resolvable surface density of the particles. Thescaling of ∆f and ∆Γ with increasing centrifugal loadis nonlinear in the applied load, implying non-Hertzianbehavior [12].The same experiment was also carried out with 2, 6,

15, and 25 µm polystyrene particles. The loading curvesall followed the same trend, but the relative shifts in ∆f

4

and ∆Γ differed based on particle size. The results fromthese loads are summarized in TBL. I.

Frequency and Bandwidth Shiftsd [µm] ∆f1/NL ∆Γ1/NL ∆f90/NL ∆Γ90/NL

1.07p 1.61e-11 3.85e-11 6.98e-11 1.43e-101.89m 5.58e-11 6.55e-11 7.90e-10 2.43e-105.86m 4.00e-09 3.09e-09 3.43e-10 3.41e-1015.0p 1.32e-07 6.39e-08 3.99e-08 9.50e-0924.80p 5.01e-07 1.53e-07 3.26e-07 1.65e-07

TABLE I. Normalized frequency and bandwidth shifts (inHz m2 at 1 and 90 g for various particle sizes in water. Thequoted diameter d is their mean diameter. p: polystyreneparticles, m: magnetite coated polystyrene.

In contrast to the situation of free particles, we havealso studied the behavior of the CF-QCM in a regimewhere particles are rigidly coupled to the sensor by at-taching 2 µm (mean diameter d = 1.89 µm) streptavidincoated paramagnetic particles modified with biotinylated25 mer oligos to complimentary strands conjugated to theQCM gold surface via thiol bonds (see Materials). This isshown in FIG. 2(d). Note that, ∆f and ∆Γ are both neg-ative and decrease with centrifugal force in the loadingorientation. When spinning with the oligo attached par-ticles, we suspect we are not sensing the presence of theparticle directly but rather the conformational state ofthe oligonucleotide layer. Such an acceleration effect hasbeen observed before [15] [14], but only within the 2 g ori-entation difference of gravity. When the oligo layer is un-der centrifugal load, it compresses, causing the density-viscosity product to increase. This behavior is consistentwith the behavior of DNA observed on QCMs under theinfluence of gravity alone [14].

Moving from particles to viscoelastic monolayers, inFIG. 2(e), 48 kbp lambda phage DNA in STE bufferwere attached to the gold sensor electrode via a com-plimentary thiolated oligo. Previous studies have shownthat, through the use of dissipation monitoring, QCMsare sensitive to not only the adsorbed mass and viscos-ity, but the physical conformal state (“shape”) of DNAshybridized to the sensor surface [20]. In the experiment,even though the force on the lambda DNAs is on theorder of femtonewtons, we observe a strong linear de-crease (∆Γ = −2.9120(95) Hz g−1) in the bandwidth asfunction of g-force, indicating an increase in viscoelasticloss. However, under larger g-forces the sign of ∆f re-verses. The origin of this effect is not understood, butcould indicate a nonlinear viscoelastic compliance underload. The unloading configuration sees a smaller negativeresponse in ∆Γ with little effect on ∆f .

At this point we make an observation about the in-fluence of salt buffer, which was used in experimentsinvolving DNA. There are several studies [21] [22] re-garding the effects of various electrolytic buffer solutionsand their concentrations on QCM measurements, includ-ing reports of an immersion angle (and therefore grav-

ity) dependence [23]. These reports suggest this effectmay be related to the behavior of the interfacial layerand ion transport in monovalent electrolytic solutions inaccelerating frames [24] [25]. We have observed a signifi-cant contribution in the unloading configuration for STEbuffer alone (∆f = −0.3260(29) Hz g−1, and ∆Γ non-linear), which was subsequently “screened” [26] by thepresence of both oligos and lambda DNAs, making theeffect negligible in the current set of experiments. Fur-ther investigation is required to explain this precisely.With the sensitivity to both particles and monolay-

ers, the instrument raises a possibility for using beadstethered by lambda DNA as a transduction mechanismto investigate its kinetics. One such example is shownin FIG. 2(f). Streptavidin coated polystyrene particleswith a mean diameter of 24.8 µm were tethered to theCF-QCM by means of a 48 kbp lambda phage DNA.Experiments were done in STE buffer whose density re-duced the maximum force the bead could exert to about40 pN which, according to the worm-like chain model [4],should almost fully extend the lambda DNA to a lengthof 16 µm.Though the instrument has not yet been developed

enough to make accurate quantitative measurements inthis load situation, the behavior of the data is a clearindication of its potential. As the tethered bead extendsthe DNA under centrifugal force, ∆f increases and ∆Γdecreases. In the case where the DNAs are trapped andpushed between the bead and the surface, both ∆f and∆Γ increase. We have confirmed the signs of the shiftsin this scenario with 10 µm and 6 µm paramagnetic par-ticles, using a magnet to either pull or push the particlestoward or away from the sensor surface. This behavioris distinct from either the case of lambda DNA or freeparticles alone.At Fc = 40 pN, the frequency shift indicates an effec-

tive decrease in the density-viscosity product of 10 % orabout 1.5 pg. For the surface densities involved (NL =3.25× 107 particle m−2), the equivalent interfacial masslost for a fully extended lambda DNA predicted by theworm-like chain model are in the picogram range and can-not account for the more than 106 signal difference shownhere. If indeed the response is due to lambda DNA exten-sion, future experiments involving high frequency, largecentrifugal force CF-QCMs could easily detect the kinet-ics of a single tether.

Theory and Modeling

To elucidate QCM behavior for samples with discreteparticles, we have performed 2D finite element simula-tions based on steady state solutions to the incompress-ible Navier-Stokes equations. This model and its imple-mentation are described in Supplementary Note 2. Thesimulation is setup as depicted in FIG. 3(a-c). Particlesare represented as spheres (or rather cylinders, in 2D,see Supplementary Figure 1) which are moved towards

5

a tangentially oscillating boundary at the bottom of thecomputational domain, representing the QCM surface.Periodic conditions are imposed on the left and rightboundaries such that the ratio of the domain width tothe particle size determines the surface coverage and thusNL. As the particle intersects the oscillating boundaryit is truncated; we identify this truncation with a finitecontact radius rc in terms of contact mechanics.

0 500 1000 1500

coupling kL[N m−1

]

−0.1 0 0.1 0.2 0.3 0.4

−0.5

0

0.5

1

1.5P V

(a) (b) (c)

(d)

∆f/NL, sim

∆Γ/NL, sim

∆f/NL, theory

∆Γ/NL, theory

load

QCM

mL

kLξL

mq

kq

contact surface density Ac [−]

∆f/N

L,∆

Γ/N

L

[ Hzm

2]

FIG. 3. Simulation of the CF-QCM behavior. Finite elementsimulation for a 10 µm polystyrene sphere (cylinder in 2D) asa function of contact surface density Ac. Negative values ofAc indicate positive separation from the surface. Discussionin the text. (a-c): Density plot of the pressure P and velocityU distributions. Units are normalized. Note that in all situa-tions with finite contact radius, stress is annularly distributedaround the edge of the contact as per the Mindlin model [27].(main plot): Shifts in ∆f and ∆Γ. (d): Mechanical modelbased on coupled oscillators. Points on the plot are a best fitof the mechanical model to the simulation.

A plot of the simulated response in frequency andbandwidth for a 10 µm particle is depicted in FIG. 3.The spheres were modeled as polystyrene with densityρ = 1.06 g cm−3, shear modulus |GL| = 1.3 GPa, and losstangent tan δ = 0.001. The spheres are in water withdensity 1.0 g cm−3 and viscosity 1.0 mPa s. The shifts in∆f and ∆Γ are plotted as a function of a dimensionlesscontact surface density Ac, defined as the contact area ofthe sample per unit area on the oscillating boundary.

The behavior of the simulation closely matches ex-perimental observations. As the sphere approaches andmakes (weak) contact with the oscillating boundary, apositive shift in both frequency and bandwidth is ob-served. As the contact radius increases, the sphere be-comes more strongly coupled to the boundary. Theamount of energy dissipated into the particle increasesuntil ∆Γ reaches a maximum and ∆f experiences a zerocrossing. The limiting case sees a rigid attachment andthe common negative frequency shift proportional to

mass adsorption takes hold.There are two aspects of the simulation that deserve

additional consideration: (1) positive shifts in ∆f and∆Γ begin before physical contact with the oscillatingboundary and (2) for smaller particles ∆Γ > ∆f whilefor larger particles ∆f > ∆Γ. The experiment shows thesame behavior, as evidenced in TBL. I. We note howeverthat the procedure of truncation and its interpretation asfinite contact radius in the framework of contact mechan-ics utilized here on discrete objects are more accurate forlarger particles (10 µm, as shown in FIG. 3) than smallerones. We explain this in the following way. It is knownin the context of DVLO theory [28] that a micron-sizedpolystyrene sphere in water near a similarly charged goldsurface will experience a repulsive force due to electro-static double-layer effects [29] [30]. The balance betweenthis and the gravitational force determines the height atwhich the particle will be at equilibrium above the sur-face. For the relevant material parameters [28] [31] wefind that, even at 90 g, the smaller 1 and 2 µm particlesnever make contact with the surface, but “hover” at sep-arations of approximately 0.3 µm to 0.15 µm. At nonzeroseparations we posit that the sphere-surface coupling, be-ing mediated by a viscous liquid, will be dominated byloss, hence ∆Γ > ∆f . On the other hand, larger particles(∼ 10 µm and above) with significant mass will overcomethe double-layer forces and make contact with the QCMthrough a finite contact radius. In this case the couplinglosses decrease and ∆f > ∆Γ.Without mention of the actual physics of the coupling,

we observe that the finite element simulation, as well asthe experimental data, follow a simple mechanical modelbased on coupled oscillators [32] [33]. The arrangementof this mass-spring-dashpot mechanical model is shownin FIG. 3(d). Here, the resonance of the quartz crys-tal ω2

q = kq/mq is coupled to a sample load with massmL though a parallel spring kL and dashpot ξL (Voigtmodel [34]). Note that kL is not an actual spring; it issimply a coupling strength between two oscillators. Thesame is true for ξL. mL is an actual mass, though inthis model it represents a Sauerbrey mass uncorrectedfor viscoelastic properties.Using the small load approximation, the response of

the system as a function of its coupling kL can be ex-pressed as [35]

∆f + i∆ΓfF

= NL

πZq

mLωq (kL + iωqξL)mLω2

q − (kL + iωqξL) (1)

where Zq is the acoustic impedance of AT cut quartz, fFis the fundamental frequency of the resonator, and NLis a surface density (number per unit area) for discreteloads. EQN. 1 as a function of kL reproduces the responseof the finite element simulation in FIG. 3, which is a func-tion of contact surface density Ac (or in un-normalizedterms the contact radius rc). A best-fit comparison to thefinite element simulation is shown as points in conjunc-tion with the simulation in FIG. 3. See SupplementaryNote 3.

6

The mechanical model has two important limits as afunction of the contact stiffness, kL, known as strong andweak coupling. These limits occur to the left and rightof a zero crossing in ∆f at kzc = ω2

qmL.

∆ffF

= NLkL

ωqπZq

(weak, kL mLω

2q)

(2)

∆ffF

= −NLmLωq

πZq

(strong, kL mLω

2q)

(3)

where we have made the approximation that ξL kL. [35]

Strong coupling is identified with mass loading (Sauer-brey [8] behavior) and a negative frequency shift linearlyproportional mL. This behavior is the one which is mostcommonly associated with QCM measurements. Phys-ically this situation is identified with a coupling rigidenough such that the particle takes part in the oscillationof the QCM. In the opposite limit is weak coupling, alsocalled inertial loading [32], and is identified by a positivefrequency shift independent of the mass and linearly pro-portional to kL. Here, the coupling is sufficiently weaksuch that the particle remains at rest in the labratoryframe. It is “clamped” by its own inertia. [36]

Experiments with nanoindentation probes operatingon QCMs in the gas phase [12], where micron sized spher-ical tips are pressed against the sensor surface, have ob-served the same positive frequency shift as a function ofapplied force, which is identified with the lateral (sphere-plate) Hertzian spring constant. We conjecture that sim-ilar behavior will be observed in the liquid phase: thecentrifugal load will primarily act on kL. We now turnto discussion of how certain sample parameters can beextracted using this model.

DISCUSSION

The response of the QCM for different load situationsunder centrifugal force exhibits a rich and complex setof behavior. Interpretation of all signals will require ex-periments beyond the scope of this manuscript, but wecomment on a few examples where our preliminary datacan be predictive within the general model we have setforth.

The coupled oscillator model (EQN. 1), when analyzedfor samples of free particles (FIG. 1(b), FIG. 2(c), andTBL. I), suggests an avenue to allow QCMs to determinethe size of large micron-sized particles in the liquid phase.Thus far this has only been possible with nanometer-sized particles which lie within the QCM’s shear acousticwave. [37] If one plots ∆f verses ∆Γ in EQN. 1 as a para-metric function of kL, the points are found to lie on a cir-cle with radius rL. In doing so, the physical mechanismmodifying kL is removed from the problem. If we thenfit a circle to the experimentally observed ∆f -∆Γ data(plotted parametrically as a function of g-force), we canextrapolate the behavior in the strong coupling regime by

−80 −60 −40 −20 0 20 40

−20

0

20

40

60

80

100

loading

∆f =−fFNLmLωq

πZq

kzc = ω2qmL

∆f [Hz]

∆Γ

[Hz]

FIG. 4. Particle sizing. Method for sizing micron-sized par-ticles using the CF-QCM. ∆f versus ∆Γ is plotted paramet-rically as a function of g-force, and the data is fit to a circle.The point on the circle for which ∆Γ = 0 and ∆f < 0 providesan estimate of mass adsorption, and thus particle size. Re-sults for particles with diameters dactual = 1, 2, 15, and 25 µmare shown in TBL. II. Fit circle has a radius of 55.77 Hz anda center of (−37.83, 41.05)Hz.

finding the point at which ∆Γ = 0 and ∆f < 0. Knowing∆f , EQN. 3 can then be inverted to solve for either num-ber density or particle size/mass. An example of thisprocedure is shown in FIG. 4 using the same data for1 µm particles shown in FIG. 1 and 2. Inset is a table forthe same predictions done for particles with known diam-eter dactual = 1, 2, 15, and 25 µm. In all cases the surfacedensity was known and the diameter dpredicted was de-rived from the mass mL, found by inverting EQN. 3. Theresults are surprisingly accurate despite the exploratorynature of the instrument’s construction, which illustratesthe robustness of this unique methodology that CF-QCMprovides. It should also be mentioned that with knowl-edge of the way in which the g-force modifies kL, thefrequency zero crossing at kzc = ω2

qmL can be used to de-termine the mass mL without knowledge of the numberdensity NL. Finally, we comment on the potential of the

Particle Sizingdactual dpredicted

1.07p 1.23(23)1.89m 1.84(6)15.0p 13.8(13)24.8p 22.6(46)

TABLE II. Results of the particle sizing method applied toparticles with diameters dactual = 1, 2, 15, and 25 µm.

7

CF-QCM technique to be sensitive to different viscoelas-tic properties of discrete samples. While the mechan-ical properties seen in biomaterials spans an enormousrange [38], we choose three general categories to highlightpotentially interesting sensor responses. As per FIG. 5these are: cells [39], agarose microparticles [40] [41], andprotein microcrystals [42]. Each is treated in the finiteelement simulation as a discrete sphere, with complexshear modulus GL = G′L + G′′L, where G′L is the storagemodulus related to elasticity, and G′′L is the loss modu-lus related to viscosity. GL is related to viscosity ηL byηL = GL/(iωq). The shifts in frequency ∆f and band-width ∆Γ are again plotted as a function of the dimen-sionless contact surface density Ac. A fictitious negativeAc is identified with a finite separation distance from thesimulated QCM surface. In all cases the coverage ratiowas 50 %, and furthermore we assume that centrifugalforce will act to “push” the sample into the QCM sur-face, increasing Ac and thus the rigidity of its contactwith the QCM.

−0.2 0 0.2 0.4−1

−0.5

0

0.5

1(a)

∆f,∆

Γ[H

z]

∆f ∆Γ

−0.2 0 0.2 0.4−1

−0.5

0

0.5

1(b)

∆f,∆

Γ[H

z]

∆f ∆Γ

−0.2 0 0.2 0.4−1

−0.5

0

0.5

1(c)

contact surface density Ac [−]

∆f,∆

Γ[H

z]

∆f ∆Γ

FIG. 5. Simulated response for different materials. Fi-nite element simulation of normalized ∆f and ∆Γ for threecategories of samples as a function of contact surface den-sity, Ac. Negative values indicate the sample has notmade contact with the sensor surface. The samples are(a) cells, GL = (10 + 50i) kPa, (b) agarose microparticles,GL = (78 + 78i) kPa and (c) lysozyme microcrystals, GL =(0.659 + 0.235i) GPa.

As can be seen, the simulated response of the CF-QCM is markedly different in each case. Cells, shownin FIG. 5(a), are assigned a shear modulus of GL =(10 + 50i) kPa and density ρL equal to the surroundingliquid medium. The high loss modulus and low storagemodulus predict the cell will exhibit shifts characteris-

tic of a viscous fluid. Likewise, the simulation shows ∆fand ∆Γ decrease and increase linearly proportional tothe contact parameter, beginning before physical contactoccurs. The proportionality is a simple function of theshear modulus and density in the semi-infinite approxi-mation [43] [9]

∆f + i∆ΓfF

= iπZq

√ρLGL (Ac) (4)

Cells in and of themselves span a large range of viscoelas-tic properties which have been demonstrated to be pre-dictive for diseases such as cancer [44]. If one knows theway with which Ac is modulated by an applied force (e.g.viscoelastic compliance), linear fitting to the CF-QCMresponse will recover GL or ρL.Next, FIG. 5(b) shows the simulated response of

agarose microparticles with a complex shear modulus ofGL = (78 + 78i) kPa. Again the density was assumedto be the same as the surrounding medium. Similar tothe viscous behavior of cells, ∆Γ decreases linearly withAc. In this sample however, an equally large elastic term,G′L, precludes the equally linear decrease in ∆f seen forcells. Instead, ∆f increases slightly before contact anddecreases slightly.At the end of the spectrum, FIG. 5(c) are lysozyme

microcrystals. These microcrystals are “hard”, hav-ing been assigned a complex shear modulus of GL =(0.659 + 0.235i) GPa. The response of these is similarto what we experimentally observe with polystyrene mi-croparticles (GL = 1.3 GPa). When the microcrystal en-ters the acoustic evanescent wave, there is an initial neg-ative shift as the effective viscosity-density product in-creases. At small contact parameters there is a positiveshift in ∆f and ∆Γ. Increasing the contact parameter,∆Γ sees a maximum and ∆f a zero crossing. As themicrocrystal becomes strongly coupled to the QCM, thefamiliar negative ∆f is recovered which, as in FIG. 4, canbe used to determine the particle size or mass.We have observed the QCM sensorgram under the

influence of centrifugal force for samples such as DNAmonolayers, free discrete polystyrene particles, and par-ticles tethered to the QCM electrode with lambda DNA.We present simulations and a theoretical framework tointerpret the QCM signals in the context of the sample’sproperties.The data presented thus far points to a potentially

interesting avenue for the investigation of force onbiomolecules using a quartz crystal microbalance. In ad-dition to the data discussed, we have also observed othertypes of signals in some of our datasets within the over-all trend shown here, which we suspect may be relatedto ionic transport [24] [25], the conformal state of DNA,and nonlinear viscoelastic behavior. Objects such as mi-croparticles attached or tethered to a biopolymer on theQCM surface become inertial transducers through whichone can extract mechanical and thermodynamic proper-ties of the macromolecules. Furthermore, the techniqueis applicable to microscopic biological objects such as

8

viruses, bacteria, and cells where measurements of me-chanical properties and their changes have been directlylinked to disease [45] [46] [47].

The enhanced signal for most samples under centrifu-gal load points to a interesting avenue of increasing thesensitivity of a state of the art QCM biosensor. This istrue even with the present state of our instrument, whichis limited to low-g regimes when compared to other com-mercial centrifuges. With operation below 90 g, we haveobserved sensitivity increases corresponding to changesof 10 % in the density-viscosity product for viscoelasticloads, and up to a factor of 10 increase in sensitivity fordiscrete particles. However, there is no technical reasonwhy future incarnations could not spin much faster andconsiderably clarify the CF-QCM sensogram. There arealso possibilities in using this platform in other relatedmodalities such as the nanotribological effects of slidingfriction [48] caused by orienting the crystal at an angleto the applied centrifugal force, propelling biomoleculesacross the surface.

METHODS

The experimental setup used a 25 mm diameter 5 MHzgold coated crystal in combination with an SRS QCM200PLL based driver circuit. On the sensing side of the crys-tal is a 125 µL PDMS/glass cell containing the specimenunder investigation. The cell is made of a thin o-ring ofPDMS (Sylgard 184, 10:1 ratio, cured 20 min at 120 C)OD = 25 mm, ID = 15.5 mm in contact with the sensingside of the crystal and covered with 25 mm round No

¯ 1coverglass, nominal thickness 0.15 mm. The non-sensingside of the crystal remains in air and is isolated fromthe body of the centrifuge. The quartz crystals are al-ways cleaned before use by immersion in fresh piranhasolution (3:1 mixture of 97 % H2SO4 and 30 % H2O2) for5 min and rinsing liberally with pure water.Free particles (Spherotech SVP-10-5, SVM-15-10, and

SVP-200-4), of different diameters were prepared by di-luting a solution of 30 µL particles in 300 µL H2O. A125 µL aliquot of the 300 µL volume was then placedin the PDMS cell in contact with the sensing side ofthe crystal. The sensing area was calculated to be1.195 cm2. The particles in solution experience a buoy-ant force which reduces their apparent mass. The surfacedensity NL was determined by counting the average num-ber of particles per unit area with a microscope and wasfound to be within 20 % of the value predicted by thevolume concentration.

For experiments involving oligos, the crystals werefirst immersed in a 1 µM solution of thiolated oligos (5’-ThioMC6-TTT TTT TTT CAC TAA AGT TCT TACCCA TCG CCC-3’) in a 1 M potassium phosphate buffer,

0.5 M KH2PO4, pH 3.8 for 1 h. Following, immersion in1 mM 6-Mercapto-1-hexanol (MCH) was used to blockresidual reactive sites on the gold electrode. After rins-ing, attachment to the prepared particles was done inSTE buffer: 1 M NaCl with 10 mM Tris buffer, pH 7.4and 1 mM EDTA. A complimentary strand (5’-biotin-CT CAC TAT AGG GCG ATG GGT AAG AAC TTTAGT-3’) was attached to the streptavidin coated par-ticles. The particles were first washed two times byalliquoting a 100 µL base solution of particles in 100 µLSTE buffer, 5000 RPM for 3 min and decanting the su-pernatant. The particles were resuspended in 20 µL ofSTE buffer and 10 µg of oligos were added. The mixturewas incubated 15 min at room temperature under slowvortexing, then washed again and resuspended in 100 µLSTE buffer. The oligo attached particle suspension wasallowed to attach to the gold surface for 15 min beforespinning.Lambda DNAs were prepared by combining 50 µL of

lambda DNA at 500 µg mL−1, 5.5 µL of 10x T4 ligase, and0.5 µL of diluted 10 µM thiolated linker oligonucleotideand heating to 70 C for 5 min. The suspension was leftto cool to room temperature as the litigation of the oligosto the DNA COS ends occured. Once the mixture was atroom temperature, 15 µL 10x ligase buffer, 127 µL H2O,and 2 µL T4 DNA ligase was added to the annealed linker.The reaction was allowed to proceed at room temperaturefor 3 h.

ACKNOWLEDGMENTS

The authors acknowledge the work of D. Schaak inpreparing and determining the protocols for the biolog-ical samples and C. Stokes for building the supportingelectronics and data acquisition hardware.This work was supported by the Max Plank Society,

the International Max Planck Research School for theScience of Light, and the Rowland Institute at HarvardUniversity.

AUTHOR CONTRIBUTIONS

A.W. carried out the experiments and wrote themanuscript. Y.S. conceived the idea and supervised theexperiment. F.V., Y.S., and A.W. planned the experi-ment. F.V. supervised the data analysis.

COMPETING FINANCIAL INTERESTS

The authors declare no competing financial interests.

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